Three-Dimensional (3D) high-speed imaging and
fabrication system based on ultrafast optical pulse
manipulation
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Citation
Kim, Daekeun, and Peter T. C. So. “Three-dimensional (3D)
high-speed imaging and fabrication system based on ultrafast
optical pulse manipulation.” Multiphoton Microscopy in the
Biomedical Sciences IX. Ed. Ammasi Periasamy & Peter T. C.
So. San Jose, CA, USA: SPIE, 2009. 71831B-8. © 2009 Society
of Photo-optical Instrumentation Engineers.
As Published
http://dx.doi.org/10.1117/12.810910
Publisher
Society of Photo-optical Instrumentation Engineers
Version
Final published version
Accessed
Thu May 26 08:47:52 EDT 2016
Citable Link
http://hdl.handle.net/1721.1/54817
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Article is made available in accordance with the publisher's policy
and may be subject to US copyright law. Please refer to the
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Detailed Terms
Three-Dimensional (3D) High-Speed Imaging and Fabrication System
Based on Ultrafast Optical Pulse Manipulation
Daekeun Kim*a and Peter T. C. So a,b
Mechanical Engineering and bBiological Engineering, Massachusetts Institute of Technology
77 Massachusetts Avenue, Cambridge, MA 02139, USA
a
ABSTRACT
Laser scanning systems for two-photon microscopy and fabrication have been proven to be excellent in depth-resolving
capability for years. However, their applications have been limited to laboratory use due to their intrinsic slow nature.
The recently introduced temporal focusing concept enables wide-field optical sectioning and thus has potential in both
high-speed 3D imaging and 3D mass-production fields. In this paper, we use the ultrafast optical pulse manipulation to
generate two-photon excitation depth-resolved wide-field illumination (TPEDRWFI). The design parameters for the
illumination were chosen based on numerical simulation of the temporal focusing. The imaging system was
implemented, and the optical sectioning performance was compared with experimental result.
Keywords: Two-photon excitation, temporal focusing, 3D lithography, high-speed 3D imaging
1. INTRODUCTION
The two-photon excitation fluorescence microscopy [1, 2], as well as two-photon excitation microfabrication [3-5], have
been widely used since it can generate finer 3D images or features than conventional wide-field microscopy and two
dimensional (2D) lithography and achieve submicron optical or fabrication resolution. Laser scanners are commonly
used to achieve this intrinsic optical sectioning capability based on spatially focusing laser light at the focal point of a
high numerical aperture objective. They have broad range of applications in the fields of 3D tissue imaging [6, 7], 3D
optical storage [8], tissue scaffold [9], photonic crystal structure [10], and microfluidic devices [11]. However, spatially
focused laser spot should be scanned laterally on the sample, resulting in taking long time to complete imaging and
fabrication. This limits two-photon excitation system to laboratory use such as microstructure prototyping and ex-vivo or
in-vitro imaging despite the very attractive submicron optical lateral resolution and optical sectioning capabilities.
Therefore, high-speed two-photon excitation technology has been needed to enable mass production and large volume
imaging to be commercially available. Several techniques have been proposed to make imaging and fabrication faster
than single focus laser scanning. Line scanning [12] gives lower optical resolution than spot scanning in spite of the easy
implementation. The use of multiple foci [13] was proposed, but it causes registration problem between patterns written
by different foci. Illumination by interference patterns on the specimen [14] is also quite useful, but its applications are
limited since it generates periodic illumination patterns both laterally and axially.
The recently introduced temporal focusing [15, 16] disperses optical pulse into monochromatic waves at different angles
on a grating surface and recombines them at focal plane. It is very useful in two-photon excitation depth-resolved widefield illumination (TPEDRWFI), since the original optical pulses are restored only at focal plane, and several
applications in the nonlinear microscopy were proposed [17-20]. However, depth discrimination capability for
TPEDRWFI system has not been fully evaluated both theoretically and empirically despite being one of the most
important parameters in TPEDRWFI design. Moreover, temporal focusing has not yet been applied to 3D lithographic
microfabrication, even though it was originally developed for imaging.
*dkkim@mit.edu; phone 1 617 253-2223; fax 1 617 324-7554; web.mit.edu/solab
Multiphoton Microscopy in the Biomedical Sciences IX, edited by Ammasi Periasamy, Peter T. C. So,
Proc. of SPIE Vol. 7183, 71831B · © 2009 SPIE · CCC code: 1605-7422/09/$18 · doi: 10.1117/12.810910
Proc. of SPIE Vol. 7183 71831B-1
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In this proceeding, we proposed 3D high-speed imaging and fabrication system based on TPEDRWFI. Manipulating
ultrafast optical pulse spatially generates temporal focusing, which enables imaging and lithographic process to be
depth-resolved with wide-field illumination. We also derive a mathematical model, based on diffraction theory, to
predict the axial optical resolution for the two-photon excitation depth-resolved wide-field illumination, and review the
design parameters based on numerical simulations to improve axial optical resolution. We implemented the proposed
system, and compared experimental result with theoretical calculation in terms of axial optical resolution.
2. TWO-PHOTON DEPTH-RESOLVED WIDE-FIELD ILLUMINATION THEORY
2.1 Principle of temporal focusing
In general, focusing is the process in which the light is concentrated tightly in the space and generates very high power at
the focus. With monochromatic wave, there is a unique type of focusing called spatial focusing. With the advent of
pulsed laser, another type of focusing has been recently introduced, i.e. temporal focusing. Optical pulse generated by
the pulsed laser has bandwidth, which is the set of numerous monochromatic waves. Light does not need to be tied in the
space. The only requirement is that all monochromatic waves arrive sharply on the focal plane at the same time.
Otherwise, optical pulse is temporally broadened and it no longer generates high instantaneous power. To realize
temporal focusing, the optical pulse should be dispersed angularly at the conjugate plane of focal plane. Any angular
dispersive element such as diffraction grating, prism, acousto-optic modulator (AOM), and even spatial light modulator
(SLM) can be used to manipulate light spatially. In this paper, diffraction grating was selected. This is because it gives
high angular dispersion, which ensures tight temporal focusing. It is also cost-effective since optomechanical
components are not required in this design.
Simplified diagram of 3D lithographic microfabrication system is shown in figure 1. It includes diffraction grating, tube
lens and the objective. First, ultrafast optical pulse is transmitted through the grating. Since ultrafast optical pulse
consists of multiple wavelengths in the bandwidth, it is dispersed at different angles, depending on wavelength
components of the ultrafast optical pulse. As seen in the diagram, its red component is dispersed more than the blue one.
Monochromatic waves propagate along different optical paths through lenses. At the focal plane, all the monochromatic
waves are combined, which results in restoring them to the ultrafast optical pulse at the focal plane. Out of focal plane,
the optical pulse becomes broader than the original one due to the phase mismatch between monochromatic waves, and
broad pulse width causes the two-photon excitation intensity to decrease. Therefore, optical sectioning capability can be
achieved by controlling optical pulse width. This is different from optical sectioning by the spatial focusing since axial
optical resolution is limited by the diffraction regardless of the optical pulse width. In next section, axial optical
resolution which determines magnitude of optical sectioning is discussed theoretically.
x
Transmission
Tube
Lens
Gratin.L
Aperture
I,
d=1/G
Objective
IPlane
-
(z=O)
-r-
I
I
Optical Pulse with
Bandwidth=FWHM
fi
II
V
fi
Field of
View=D
Numerical
apuerture=NA
uII
IuIII
f2
f2
uI
Fig 1. Simplified diagram of two-photon excitation depth resolved wide-field illumination model based on spatial light
manipulation. It consists of diffraction grating, tube lens and objective. For the illustration purpose, three different
color beams are shown.
2.2 Mathematical model for two-photon excitation depth-resolved wide-field illumination
In order to optimize the design of the 3D lithographic microfabrication system, it is important to thoroughly understand
the image formation theory underlying this approach. We derive an optical model of light distribution near the focal
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plane based on diffraction theory [21-24] to evaluate axial optical resolution with axial intensity distribution. This optical
model allows us to accurately predict the axial optical resolution that can be achieved. Furthermore, it makes us examine
the effects of different design parameter choices in optimizing depth-resolved capability.
Figure 1 shows how each wave propagates through an optical system. To simplify this model, the following assumptions
are applied: 1) the optical model is diffraction-limited. 2) all the lenses are perfectly chromatic-aberration-corrected. 3)
dispersion occurs only at the diffraction grating. 4) the input beam profile is Gaussian with a width of S (1/e beam
radius), 5) the spectral distribution of the input beam is also Gaussian with a bandwidth of K in terms of wavenumber,
and 6) the ultrafast optical pulse is chirp-free. Then ultrafast optical pulse can be defined as below:
r r
+∞
+∞
r
i ( k ⋅ r −ωt )
U ( x, y, z , t ) = ∫ U ( r , k ) e
d ω = c ∫ U ( x, y ) eikzW ( k ) e − ikct dk
−∞
−∞
(1)
⎛ x +y ⎞
⎛ Δk 2 ⎞
=
exp
and
W
k
B
( ) 0 ⎜ 2⎟
⎟
S2 ⎠
⎝
⎝Κ ⎠
2
where U ( x, y ) = A0 exp ⎜ −
2
A0 and B0 are the amplitudes, and Δk = k − k 0 is the difference between k =
2π
=
ω
, the wavenumber for the given
c
wavelength and k0 , the wavenumber for the center wavelength. Moreover, λ is wavelength, ω is optical angular
frequency, and c is the speed of light. Since diffraction theory is valid for monochromatic wave, divide and conquer
(D&C) method is applied: optical pulse separates into monochromatic wave components, the electromagnetic wave
fields are calculated with diffraction theory, and they merge into the optical pulse in time domain at the focal plane. For
each k , the transverse field for each at grating surface [25] can be written as:
λ
U1 ( xi , yi , k ) = U ( xi cos α , yi ) ⋅ exp {i ⋅ Δk sin α 0 ⋅ xi }
(x , y )
i
i
(2)
is the lateral coordinate at the grating plane. The grating effectively introduces a phase chirp along one
direction. α 0 = sin
−1
( 2π G / k )
0
is the incident angle to the grating with groove frequency G such that the center
wavelength of the input beam propagates along the optical axis. Since the grating and the microscope focal plane is
conjugated by a 4-f imaging system, the field can be readily propagated along the optical path. Ignoring the field
aperture of the microscope, the field at back aperture of the objective is
U 2 ( xb , yb , k ) = −ik
exp {ik 2 f1 }
2π f1
+∞
∫ ∫
−∞
+∞
−∞
⎧
U 1 ( xi , yi , k ) exp ⎨ −ik
⎩
xb xi + yb yi ⎫
f1
⎬ dxi dyi
⎭
(3)
f1 is the focal length of the tube lens, and ( xb , yb ) is the lateral coordinate of the back aperture plane. When the waves
propagate into the objective, the back aperture size in the objective should be considered, and it is incorporated as:
⎛ xb2 + yb2
U 3 ( xb , yb , k ) = U 2 ( xb , yb , k ) ⋅ circ ⎜
⎜ D/2
⎝
⎞
⎟
⎟
⎠
⎧ 1 for r < 1
⎪
where circ ( r ) = ⎨1 / 2 for r = 1
⎪ 0 Otherwise
⎩
(4)
D is the diameter of the back aperture in the objective. The field near the focal plane of the objective can be calculated
as:
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U4 ( xf , yf , z f , k )
= −ik
(x
f
exp {ik ( 2 f 2 + z f
)}
2π f1
, yf , zf
+∞
∫ ∫
−∞
+∞
−∞
⎧
U 3 ( xb , yb , k ) exp ⎨ −iπ
⎩
⎫ ⎧ x f xb + y f yb ⎫
⎬ exp ⎨ −ik
⎬ dxb dyb
f2 ⎭
f2
⎩
⎭
2
2
xb + yb z f
f2
(5)
) is the coordinate placed on the focus of the objective. Since the tube lens and the objective are chromatic-
aberration-corrected, the effective optical path lengths (phase terms) are same for the different wavenumber k at the
focal plane.
exp {i 2k ( f1 + f 2 )} = const
(6)
To reconstruct the optical pulse, all the monochromatic waves delivered to focal plane of the objective in vector form
since they propagate along different path. Therefore, the temporal evolution of the field around focal plane can be shown
as:
r
U5 ( x f , y f , z f , t ) =
c
∫
+∞
−∞
r
r
U 4 ( x f , y f , z f , k ) ( x f sin β ′ ( k ) + z f cos β ′ ( k ) ) W ( k ) exp ( −i ( kct − φ ( x f , y f , k ) ) dk
where
⎛
φ ( xf , zf , k ) = k ⎜
zf
⎝ cos β ′ ( k )
[1 − sin α
(7)
⎞
0
⋅ M sin β ′ ( k )] − sin α 0 ⋅ Mx f ⎟
⎠
β ′ ( k ) is the incident angle for each k with respect to optical axis after objective, φ ( x f , z f , k ) is the pulse front delay
which comes from diffraction grating, and M =
f1
f2
is magnification with the lenses. Time-averaged intensity close to
the focal plane can be expressed as:
I ( xf , yf , z f ) = fp ∫
1
fp
0
2
r
U 5 ( x f , y f , z f , t ) dt
(8)
f p is repetition rate of the ultrafast pulsed laser. Since multiphoton excitation is a nonlinear process, multiphoton
excitation efficiency is proportional to Nth power of the intensity with N-photon excitation process.
I N ( xf , yf , zf ) = fp ∫
0
1
fp
2N
r
U 5 ( x f , y f , z f , t ) dt
(9)
In case of two-photon process in the system, N =2. With axial intensity profiles obtained in eq. (9), axial optical
resolution can be calculated.
3. TWO-PHOTON DEPTH-RESOLVED WIDE-FIELD ILLUMINATION EVALUATION
3.1 Simulation for optical axial resolution evaluation
Figure 2 represents simulation results of the axial optical resolution for two-photon depth-resolved wide-field
illumination system with following different design parameters (also shown in red in figure 1.): field of view radius
(r=D/2), focal length of the tube lens (f1), the bandwidth of ultrafast optical pulse (FWMH λ), groove frequency of
diffraction grating (G=1/d), and the numerical aperture (NA) of the objective (NA). In this paper, axial optical resolution
is defined as full-width-at-half-maximum (FWHM) of axial intensity profile.
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0
0
0
I of Axial Resolution (Itm)
=
LI
0.1
50
150
100
200
Field of View Radius Size (Lm)
(a)
250
E
-S- G=150mm'
-0-- G=3OOmrn
200
-- G=6OOmri
0
-- G=12OOmm
T
r
-- -----4-
4-
0 150
Cl)
a,
100
Ca
0
=
50
0
LI
100
200
300
400
500
600
Tube Lens Focal Length (mm)
(b)
40
E
-- G=150mm'
30
-1
20
I
x 10
-0- G=3OOmm
-y-- G=6OOmm
-A-- G=l2OOmm
-I--1
=
U-
0
20
40
60
80
100
Optical Pulse Bandwidth (nm)
(c)
Fig 2. The simulation results of axial optical resolution for the given parameters in the depth-resolved wide-filed
illumination system: (a) axial optical resolution along r depending on G, (b) axial optical resolution along f1
depending on G, and (c) axial optical resolution along FWHMλ depending on G.
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In the simulation, we found interesting behaviors with different parameters. As shown in the figures 2(a), field of view
(FOV) size is independent of G with large enough FOV. Axial optical resolution seems to be improved as FOV radius
size becomes smaller than 10µm, but smaller FOV approaches to spatial focusing spot size, and it is not wide-field
illumination any more. Thus it makes sense that small FOV which approaches to the focal spot provides diffractionlimited axial optical resolution. In the figures 2(b), axial optical resolution is inversely proportional to f1, and it is still
valid for different Gs and FWMHλs. In addition, axial optical resolution is also inversely proportional to FWHMλ, as
shown in figures 2(c). It is noted that the optical resolution has asymptotical value (about 750 nm) with large G or
FWMHλ, which is close to diffraction limit of spatial focusing spot with given NA of the objective. This is because some
of wavelength-resolved light (far-red or far-blue in the ultrafast optical pulse) is clipped due to size of back aperture of
the objective determined by NA, even though the optical pulse with large FWHMλ is very narrow.
To summarize, FOV size is irrelevant of optical resolution as long as the system maintains wide-field illumination.
Angular dispersion (dispersion angle per wavelength), which can be controlled by f1 and G, is the most important design
parameter to optimize axial optical resolution, but is limited by diffraction limit associated with NA. Therefore, angular
dispersion determined by G and FWHMλ is one of the key factors to control the axial optical resolution, which is also
diffraction limited.
3.2 Comparison between simulation and experiment result for axial optical resolution
iCCD : Intensified Charge-Coupled Device
iCCD
Beam Splitter
Reflective
Diffraction
Grating
Tube
Lens
Objective
Specimen
Ultrafast Optical Pulse
from Ti:Sa laser
Fig 3. Schematic diagram for two-photon excitation depth-resolved wide-filed illumination system. The ultrafast optical
pulse (780nm, ~ 100 fs) was delivered from tunable Ti:Sapphire pulsed laser. To control illumination field of view,
beam expander is used. Reflective diffraction grating disperses the optical pulse in the space, and it is restored after the
high NA objective at the focal plane. Fluorescence signal is collected backward, and it is detected with intensified CCD
(iCCD) at the image plane.
To validate the simulation results, axial optical resolution should be measured after TPEDRWFI is set up. As a light
source, the ultrafast optical pulse (the center wavelength of 780 nm, the pulse width of about 100 fs, and repetition rate
of about 80 MHz) was delivered from the tunable Ti:Sapphire pulsed laser (Tsunami, Spectra-Physics, Mountain View,
CA) pumped by the diode-pumped solid-state (DPSS) laser (Millennia Xs, Spectra-Physics, Mountain View, CA). The
beam diameter can be controlled with the beam expander, resulting in scaling the field-of-view on the specimen. At the
surface of the reflective diffraction grating with the groove frequency of 600 g/mm (53004BK02-35IR, Richardson
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Grating Lab, Rochester, NY), ultrafast optical pulse is dispersed spatially, and it is restored after the objective (Fluar,
403/1.30 Oil, Zeiss MicroImaging, Thornwood, NY) in the inverted microscope (Axiovert S100TV, Zeiss MicroImaging,
Thornwood, NY) through NIR achromatic doublet with the focal length of 250mm (AC254-250-B, Throlabs, Newton,
NJ) used as a tube lens to reduce chromatic aberration. The fluorescence on the specimen is collected backward through
the objective. At the beam splitter (700dcxr, Chroma Technology, Rockingham, VT), the fluorescence is reflected, and it
is imaged at the intensified CCD (PI-MAX, Princeton Instrument, Trenton, NJ). Specimen is placed on the stage
controlled laterally in the submicron range, and the objective is also controlled axially by piezoelectric actuator to move
the focal plane at the specimen.
a)
P
cP
P
4-
maIized Intensi
Co
C
C
P
C
malized Intensity (a.u.)
To measure optical resolution, 0.1µm diameter yellow-green (505/515) fluorescent polystyrene microspheres (F-8803,
Invitrogen, Carlsbad, CA) were used, each of which can be considered as a point light source. Figure 4 shows the axial
optical resolution in the simulation with design parameters from the developed system and the axial optical resolution in
the experiment. Measured resolution (figure 4(b)) is very close to simulated resolution (figure 4(a)). It confirms that the
simulation results are well matched with measurement and shows the potential to achieve diffraction-limit optical
resolution practically with different design parameters.
z00
0.2
0
0.0
0.0
-4
-2
0
2
4
-4
-2
0
2
4
Position (jim)
Axial Position (I.tm)
(a)
(b)
Fig 4. Axial resolution with 0.1µm fluorescent microsphere: (a) axial optical resolution from the numerical simulation (b)
axial optical resolution from the measurement (red dots), which is fitted to Lorentzian function (blue line).
4. CONCLUSION
In summary, TPEDRWFI can be applied to both imaging and fabrication systems. First, mathematical model for
TPEDRWFI was derived based on optics theory. With this model, numerical simulation was performed to figure out the
dominant parameters for determining axial optical resolution and to optimize the proposed system design. Depthresolved wide-field microscopy was incorporated with image sensor, and simulation results were well matched with
axial optical resolution measurements. In the future, it will lead to using high-speed imaging with high sensitivity in the
live cell such as image correlation spectroscopy (ICS) applications, and 3D lithographic microfabrication in the
photonics and biomedical applications such as 3D optical circuit with photonic crystal structures and 3D tissue scaffold
for artificial organ regeneration.
ACKNOWLEDGEMENT
This work is supported by MIT Deshpande Center for Technology Innovation.
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